UPTEC ES11 031
Examensarbete 30 hp
December 2011
Flywheel energy storage
a conceptual study
Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student
Abstract
Flywheel energy storage - a conceptual study
Rickard Östergård
This master thesis was provided by ABB Cooperate Research in Västerås. This study has two major purposes: (1) to identify the characteristics of a flywheel energy storage system (FESS), (2) take the first steps in the development of a simulation model of a FESS.
For the first part of this master thesis a literature review was conducted with focus on energy storage technologies in general and FESS in particular. The model was developed in the simulation environment PSCAD/EMTDC; with the main purpose to provide a working model for future studies of the electrical dynamics of a FESS. The main conclusion of the literature review was that FESS is a promising energy storage solution; up to multiple megawatt scale. However, few large-scale installations have so far been built and FESS is not a mature technology. Therefore further research and development is needed in multiple areas, including high strength composite materials, magnetic bearings and electrical machines. The model was implemented with the necessary control system and tested in a simulation case showing the operational characteristics.
Sponsor: ABB
ISSN: 1650-8300, UPTEC ES11 031 Examinator: Kjell Pernestål
Ämnesgranskare: Hans Bernhoff Handledare: Frans Dijkhuzien
SAMMANFATTNING
Detta examensabete har två huvudsyften: (1) att identifiera och beskriva de ingående
komponenterna hos ett energilagringssystem med svänghjul (Flywheel Energy Storage
System, FESS), (2) ta första stegen i utvecklingen av en simuleringsmodell.
Första delen av examenarbetet genomfördes genom en litteraturstudie med fokus på
energilagringsteknik i allmänhet och FESS i synnerhet. Modellen är utvecklad med hjälp
av simuleringsprogrammvaran PSCAD/EMTDC med huvudsyftet att uveckla en
fungerande modell för framtida studier av den elektriska dynamiken hos ett FESS.
Den viktigaste slutsatsen av litteraturstudien är att FESS är en lovande
energilagringsteknik med kapacitet upp till flera megawatt. Hittills har endast ett fåtal
storskaliga installationer byggts, vilket betyder att FESS inte är en mogen teknik. Det
behövs därför vidare forskning och utveckling inom flertal områden; bland annat inom
materialvetenskap, magnetiska lager och generatorer.
Simuleringsmodellen har implementerats med nödvändiga styrsystem och testats i ett
simuleringscase som visar de viktigaste egenskaperna hos ett FESS.
TABLE OF CONTENTS
1 INTRODUCTION ... 3
1.1 BACKGROUND ... 3
1.2 SMART GRID ... 3
1.3 AIM ... 4
2 ELECTRICAL ENERGY STORAGE SYSTEMS (ESS) ... 5
2.1 APPLICATION IN ELECTRICAL GRIDS ... 5
2.2 ENERGY STORAGE TECHNOLOGIES ... 6
2.2.1 Pumped hydro (PHS) ... 7
2.2.2 Compressed air energy storage (CAES) ... 7
2.2.3 Battery energy storage (BESS) ... 8
2.2.3.1 Sodium Sulphurs Batteries ... 8
2.2.3.2 Lithium-Ion Batteries ... 8
2.2.3.3 Lead-acid batteries ... 8
2.2.3.4 Flow batteries ... 9
2.2.4 Super conducting magnetic energy storage (SMES) ... 9
2.2.5 Supercapacitors... 10
2.3 TECHNOLOGY SUMMARY ... 10
3 FLYWHEEL ENERGY STORAGE ... 11
3.1 GENERAL ... 11
3.2 HISTORY ... 11
3.3 FLYWHEEL BASICS... 11
3.3.1 Geometries and material ... 12
3.4 FLYWHEEL SYSTEMS COMPONENTS ... 14
3.4.1 Electrical machine... 14
3.4.2 Bearings ... 14
3.4.3 Housing ... 15
3.4.4 Power electronic interface ... 16
3.5 RANGE OF CAPACITIES ... 16
3.6 ENVIRONMENTAL ISSUES ... 16
3.7 COMMERCIALLY AVAILABLE FLYWHEEL SYSTEMS ... 16
3.7.1 Beacon Power ... 17 3.7.2 Vycon Energy ... 18 3.7.3 Piller ... 18 3.7.4 Active Power ... 19 3.7.5 Market summary ... 19 3.8 SUMMARY ... 20 4 MODEL DESIGN ... 21 4.1 SCOPE ... 21 4.2 MODEL DESCRIPTION ... 21
4.3 SINUSOIDAL PULSE WIDTH MODULATION ... 21
4.4 D-Q-0 TRANSFORMATION ... 22
4.5 MOTOR/GENERATOR ... 23
4.5.1 Machine-side VSC control strategy ... 24
4.5.2 Grid connected VSC Model ... 26
4.5.3 Grid-side VSC control strategy ... 27
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5 SIMULATION ... 29
5.1 CASE STUDY ... 29
5.2 SIMULATION RESULTS ... 31
6 CONCLUSIONS AND DISCUSSION ... 32
7 RECOMMENDATIONS FOR FUTURE WORK ... 33
8 ACKNOWLEDAGEMETS ... 34
9 REFERENCES... 35
3
1
INTRODUCTION
1.1 Background
Renewable energy technologies are an effective answer in the effort to reduce CO2 emissions. In an
electrical system the supply and demand must be in balance to keep the electrical grid stable. Since most renewable energy, for example wind and solar power, are of intermittent nature the production cannot be controlled. The supply varies with season, time and weather conditions. The ever-increasing demand and need for renewable energy sources, dictates new requirements for the electrical grid. Important aspects as power system stability, reliability and power quality must be ensured when more intermittent energy sources are being installed. These requirements can be met by upgrading the grid to be more dynamic and intelligent, a so called smart grid, where energy storage devices are an important part of the solution. Unlike other forms of energy, electric energy is difficult to store in any useful quantity. Under somewhat rare circumstances, electricity can be transformed into potential energy in reversed hydro power plants. Some attempts (less than 1% of the total available storage worldwide) have been done with chemical, kinetic and thermal energy. While transmission lines and distribution grids transport electricity over land to end users, energy storage systems can move electricity through time. This ensures constant electricity supply when and where it is most needed. Energy storage systems, at the right place and properly designed can help improve electric grid reliability and efficiency.
1.2 Smart Grid
The existing electric grid systems are not designed to meet requirements of the modern society, including small scale independent generation units, increasing use of digital equipment, installations of renewable energy and introduction of a fleet of electrical vehicles. The traditional electric grid consists of large generation units far form end users and power is transferred in a main high voltage transmission grid to local low voltage distribution grids. In today’s grid topology the electricity flows mainly in one direction, as illustrated in Figure 1.1.
Figure 1.1 Today's grid topology. The power flow is mainly one-way [39].
In order to meet the demands described above todays grid topology must change into a two-way flow of both electricity and information to form a automated, widely distributed transmission grid, as illustrated in Figure 1.2. This vision for the future grid is called Smart Grid [1].
4
Figure 1.2 The future Smart Grid. The power flow is two-way [39].
The vision of the smart grid still depends on support of large-scale generation units, but it includes a considerable quantity of electric energy storage and renewable energy, both at large scale power system level and in local distribution grids. The main benefits of a future Smart Grid will include: large scale use of renewable energy source, reduction of peaks in electricity demand, more active consumers and increased efficiency in use of electrical energy. The EU’s Technology Platform for Smart grid summarizes the central objectives as follows [2]:
- Better facilitate the connection and operation of generators of all sizes and technologies. - Allow consumers to play a part in optimizing the operation of the system.
- Provide consumers with greater information and choice of supply.
- Significantly reduce the environmental impact of the whole electricity supply system. - Deliver enhanced levels of reliability and security of supply.
Energy storage systems (ESS) will play a central role in in the research and development of smart grids.
1.3 Aim
ABB is a global leader in power and automation technologies. Energy storage system for gird integration is a growing market of interest for ABB. Today they have a battery system ready for commercial deployment, but other energy storage technologies are also of interest. This master thesis is done with collaboration with ABB Cooperate Research in Västerås. The main goal of this thesis is to provide a market overview and a technical description of a flywheel energy storage system (FESS), in order to provide a basis for future research and development. The aim is to describe and identify the essential system components and highlight important aspects when designing FESS. Furthermore, this thesis aims to give a comparative overview of flywheels vs. other technologies for energy storage systems.
Additionally, an overview of commercially available flywheel energy storage system is given, together with the purpose of evaluate where the market stands and how far the technology development has come. The last part of the thesis is dedicated to developing a simulation model of flywheel energy storage A primary model design is performed with the goal to be a starting point for future studies of electrical dynamics of a FESS. A case study is carried out to show the operational principles of flywheel energy storage systems. An example of a future case study that can be performed is how a FESS can handle power quality problems associated with a wind farm.
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2
ELECTRICAL ENERGY STORAGE SYSTEMS (ESS)
The following section gives an overview of energy storage systems for storing of electrical energy. It will describe the technical characteristics and give the reader an overview of the general properties, advantages and disadvantages for each system. The aim is to give the reader background information about the alternatives to electrical energy storage with flywheels. This section gives also an overview for the applications for energy storage systems in electrical grids.
2.1 Application in Electrical Grids
Energy storage systems (ESS) can be applied to a wide range of applications in the electrical system. It can be the solution for problems in the whole electrical energy value chain, from generation support, transmission and distribution to the end-consumer users. The following list summarizes applications in electrical power systems where energy storage system can be used [3].
1. Electric energy time shift - Energy is purchased during off-peak hours when prices are low and sold at a later time when the price is high. The stored energy can also be used by the storage-owner to avoid expensive energy purchase during hours of high demand. Also known as energy arbitrage. 2. Load following – A requirement to keep the stability of the electricity grid, the storage power respond to the demand of the end-user. The storage system either produce power or consume (charge) to meet the supply and demand requirements.
3. Transmission and distribution upgrade deferral - By adding storage resources to a nearly overloaded transmission and distribution system, investments can be delayed or entirely avoided. 4. Time of use energy cost management – Refers to the same mechanism as 1 but here end-users
reduce their total costs for electricity by utilizing storage systems.
5. Electric Service Reliability - Involves energy storage to provide better reliability of electric service. In the case of a long-term power outage (more than a few seconds) the energy storage provides enough energy to either preform a safe shutdown of vulnerable equipment or ride though the entire outage.
6. Electric Service Power Quality – The energy storage is used to provide power quality services. This can improve the quality of the power to loads during short duration faults in the electrical system. Examples of poor power quality include: voltage sags, variation in frequency and harmonics.
7. Renewables energy time shift – Energy is stored to increase the value of the produced energy. If the price of energy is low when the renewable energy sources (RES) is producing the energy storage unit can provide a time-shift so the energy can be sold when the price is higher.
8. Renewable capacity firming – This application applies to intermittent RES. The energy storage provides a way to smooth the output form this type of energy source. The combined output from the energy storage and the RES is close to constant. The application is especially valuable during peak-demand periods.
6 Table 2.1 summaries these applications and gives an estimate of the different applications power and discharge specifications.
Table 2.1 Estimate of need for storage power and discharge duration for different application for ESS [3]
Application type Storage Power Discharge Duration 1 Electric energy time shift 1-500 MW 2-8 h
2 Load following 1-500 MW 2-4 h
3 Transmission and distribution upgrade deferral 250 kW - 5MW 3-6 h 4 Time of use energy cost management 1kW - 1MW 4-6 h 5 Electric Service Reliability 0.2kW - 10MW 5 min - 1 h 6 Electric Service Power Quality 0.2kW - 10MW 10 s - 1 min 7 Renewables energy time shift 1kW - 500MW 3 - 5 h 8 Renewable capacity firming 1kW - 500MW 2 - 4 h
2.2 Energy storage technologies
Electric energy has for long been a commodity where storage has been achieve efficiently in only some rare cases. However there are existing and emerging technologies that allow electric energy to be stored. Implementing a well-functioning energy storage system, which is seamlessly integrated to the grid, is not an easy task. The design of such a system must take many factors in consideration. As described in section 2.1 the applications for ESS have a variety of demands and different storage technologies are suitable for different applications. There is a vast diversity of possible energy storage technology alternatives for the electric sector, each with unique functioning, performance, cycling and durability characteristics.
To date about 100GW of electric energy storage systems is installed worldwide, where pumped hydro is the most represented technology (~127,000 MW). The next largest is compressed air energy storage with about 440 MW installed.
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2.2.2 Pumped hydro (PHS)
Pumped hydroelectric energy storage is the most widespread electrical energy storage technology in the world. The first pumped hydro station was built in Italy and Switzerland in the 1890s, thus it can be considered as a mature technology. Further it was the only commercially available large-scale energy storage until the 1970 when compressed air energy storage was introduced [4,5].
A typical pumped hydro power plant consists of two water reservoirs located on different altitudes. During off peak hours when cheap electricity is available water is pumped from the lower reservoir and stored in the higher. During times of high demand of electricity water flows, through a hydroelectric turbine, to the lower reservoir to generate electricity [3]. The quantity of stored energy is a function of the total volume of water in the upper reservoir and the differential height of between the two reservoirs. The reservoir can for example be artificially built, natural bodies of water or the open sea. The latter is only used for the lower reservoir.
The losses considered in a pump hydroelectric plant include turbulence, turbine/pump and motor/generator efficiency. The overall efficiency is about 70-85% depending on design [5].
PHS technology is mature technology but is characterized by high capital investment and strong geological barrier. This type of system is suited for applications with high power capability demand, a typical plant has the power rating of 1000-2000 MW and the discharge time is somewhere around 6-12 h [5].
Advantages include:
- Very high energy capacity - Large-scale
- Mature and commercial technology Disadvantages include:
- Strong geological barrier. - High capital investment
- Comparatively slow response time. - Comparatively low efficiency
2.2.3 Compressed air energy storage (CAES)
A CAES plant has similar design as a gas turbine power plant. The basic difference to a conventional gas turbine power plant is that the air is already compressed and the fuel consumptions can be significantly lowered. The air is compressed during off peak hours and typically stored in an underground cavern, vessel, or pipes. When the energy is needed the compressed air is mixed with natural gas and combusted in a gas turbine to generate electricity. In a conventional gas turbine power plant about 2/3 of the energy produced is consumed when pressurizing the air before combustion in the gas turbine. [5] In comparison with a conventional gas turbine plant CAES consumes 40 % less fuel producing the same electricity output. CAES usually is located near a suitable geological formation such as mines, depleted gas wells or salt caverns.
Typical compressed air power plant has a power rating in the 110-290 MW range and can deliver power for up to 10 hours [30]. There is about 440 MW installed worldwide [6]. The technology has been around since the 1970’s but only two plants have been built. The first commercial CAES plant was built in 1978 in Germany, with a capacity of 290 MW. The second commercial CAES was a 110 MW plant built 1991 in Alabama, USA. These plants are used to supply peak load power.
Current research on CAES technology focus on development of adiabatic CAES systems where the heat produced during compression is stored and reused to heat the compressed air before passing though the turbine. This would eliminate the need for fuel in the system.
8 Advantages include:
- Very high energy capacity Disadvantages include:
- Strong geological barrier. Despite many years of effort, no new suitable caverns have been found.
- Comparatively slow response time - Comparatively low efficiency
2.2.4 Battery energy storage (BESS)
Energy is stored chemically and electric energy is released during discharge through a redox reaction. A basic battery cell consists of:
- Negative electrode or anode, gives electrons and oxidized during the redox reaction. - Positive electrode or cathode, accepts electrons and is reduced during the redox reaction. - Electrolyte, supplies medium for transfer of electrons.
The two electrodes are interconnected with an external circuit, which allows charge and discharge of the cell. Depending of the desired output voltage and current multiple cells can be connected in serial or parallel. There are several technologies to store electrical energy in batteries. The oldest, classical and mature technology is Lead-acid. New technologies under development include Sodium Sulphurs and Lithium-ion [7].
2.2.4.1 Sodium Sulphurs Batteries
The sodium sulphur battery consists of positive liquid sulphur electrode and a negative sodium electrode separate by an alumina ceramic electrolyte. When the battery is discharged positive sodium ions flow though to electrolyte and electrons flows in the external circuit producing around 2 V. This process is reversed during charging; the positive sodium ions pass back though the electrolyte and reform elemental sodium. The operational temperature of a sodium sulphur battery is high, about 300 ˚C. The high temperature is required to maintain the molten states of the electrodes. The efficiency is about 80%. A typical system has a rated power of 30 MW and able to provide power during 6 hours. There is about 316 MW installed worldwide [6].
2.2.4.2 Lithium-Ion Batteries
Lithium-ion batteries consists of a lithiated metal oxide cathode and a graphite carbon anode. The electrolyte is made up of lithium salts. During charging lithium-ions from the cathode flows through the electrolyte, to the anode where the ions combine with external electrons and is deposited as lithium atoms between the carbon layers. When the battery is discharged this process is reversed. The efficiency of lithium-ion battery system is high, about 90-95%. A typical system is has a rated power at 1-10 MW [6].
2.2.4.3 Lead-acid batteries
There are many types of lead-acid batteries but all can be described by the same basic chemistry. The anode is made of lead dioxide and the cathode is made of metallic lead. The electrolyte consists of sulphuric acid, which is consumed during the discharge. The efficiency of a lead-acid battery system is about 70-80% [4]. Lead-acid battery system is the oldest and most recognized electrical energy storage today in small and medium scaled systems [5]. It has been the default choice for many small and medium scale energy storage applications despite many disadvantages like low life expectancy, low energy density, high maintenance and environmental hazards related to the handling of lead and sulphuric acid. Lead-acid battery system can be used in numerous applications; however the technology has rarely been used in large-scale energy management applications [4]. The largest installation was a 10 MW, 40 MWh energy storage plant in Californa, USA, operational during 1988-1997.
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2.2.4.4 Flow batteries
Flow battery energy storage system consists of two sets electrolytes that flow through two independent loops. The loops are joined in the cell but separated by a membrane that prevent the electrolytes from mixing but allow ion-exchange. Flow batteries have the advantage of being easy scalable, compared to conventional battery cells. The fact that the electrolytes are stored outside the cell makes it possible to increase the energy storage capacity simply by increasing the volume of the reservoirs of electrolyte. This makes the technology suitable for large-scale systems [8]. The amount of energy stored is determined by the size of the tanks [9].
There are various types of flow batteries technologies, e.g. ZnBr, Vanadium Redox and Polysulphide Bromide. An example flow battery system is 15 MW, 120 MWh and efficiency of about 75 % from Regenesys Technologies in England [9].
Advantages include:
- High power capacity - Long life
- Scalable Disadvantages include:
- Low power density - High cost
- Moving mechanical parts, for example pumps.
2.2.5 Super conducting magnetic energy storage (SMES)
SMES store energy in a magnetic field; a DC current flowing through a superconducting coil creates the field. Electric energy can be released from the system when needed. A power electronics interface is required to connect the SMES to the grid. In order to sustain low losses the coil must be kept below a critical temperature, somewhere around 4 K. The low temperature makes the resistive losses negligible [11].
The response time for a charge- discharge cycle for SMES system is in the order of milliseconds. This makes this technology suitable for power quality applications. The efficiency is high, over 90 %, however the energy used to cool the system must be considered. SEMS systems has been proposed in a wide range of energy storage capacities from 0.3 to 1000 MWh and power rating from 1 MW to 1000 MW [4,10]. Disadvantages of the SMES system are the massive electromagnetic fields that effect possible placement of the systems.
Advantages include:
- High efficiency
- Comparatively quick response time Disadvantages include:
- Massive electromagnetic fields
- Complex system due to cryogenically cooling - High costs
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2.2.6 Supercapacitors
Supercapacitors or double layer capacitor store energy much in the same way as a conventional capacitor, hence the amount of stored energy can be described by:
A double layer capacitor consists of two electrodes, a separator, electrolyte, two current collectors and housing. A very high capacitance is obtained in this way. Super capacitors are suitable for high power applications and offer very quick response times and high efficiency. Disadvantages are comparatively low energy density, high self-discharge and high cost [7, 4,8]. Small units exists, lager is under development. Typical power ratings are 1kW-250 kW and efficiencies in the ranges of 85-98% [8].
Advantages include:
- Comparatively quick response time Disadvantages include:
- High self-discharge - High cost
- Low energy density
2.3 Technology summary
Table 2.2. Summary of storage technologies [3,5,6,8,9,10].
Technology Typical Nominal Power Discharge time Respones Time Efficiency Lifetime Pumped Hydroelectric Energy
Storage
100-4000 MW 6-24 h 10s -3 min 65-85% 30-75 years
Compressed air energy storage 25-30000 MW 4- 24 h 3-15 min 50-85% 20-40
years B a tt er y Flow Batteries 25 kW-10 MW 1-8 h 30 - 100 ms 65-85% 2-10 years Lithium Ion 10 kW - 10 MW 10 min - 1 h 85-90%
Lead Acid 50 kW - 30 MW 15 min – 4 h
70-80% Sodium Sulphur 50 kW - 30 MW 1-8 h
75-90%
Supercapacitors 10 kW - 1 MW 1s - 1min 5-10 ms 85-95% 40 years
Superconduction Magnetic energy storage
1 MW - 100 MW 1s - 1min 5-10 ms 85-95% 30-40 years
Flywheels 10 kW - 20 MW 1s - 1 h 5-10 ms 85-95% 20 years
PHS- and CEAS-plants exists, however few places remain where it is feasible to build. Great environmental impact is associated with these two technologies. Flywheels, batteries, SMES:s and supercapacitors are the energy storage systems that compete in the same area, where SMES is still a research area and few commercial applications exists. Supercapacitors have lower rated power than both flywheel and battery system.
Frequency regulation is a market expected to grow with the expansion of wind and solar power. The frequency regulation market was 2010 worth US $495 million in the United States; a number expected to increase [12]. The dominant method today for frequency regulation is throttling power generation up and down, which is not efficient due to the fact that generators operate at an optimum when held steady at high
11 output. Many power plants take a minute or longer to respond to dispatch signals. Therefore, grid operators favour faster-acting regulators, such as flywheels and batteries.
Battery-based frequency regulators are cheaper per megawatt to install than flywheel and are a competitive technology. But the flywheel energy storage manufacturer, Beacon Power, believes that the apparent cost advantage of batteries will literally erode with time, as constant cycling degrades their capacity. David Hawkins, a senior principal consultant for the Netherlands-based energy consulting firm KEMA, who until 2010 was chief engineer for integrating renewable energy at California's grid operator agrees that [13]:
”…batteries will lose their edge over flywheels under that level of use. A battery really doesn't like to be totally charged and discharged, whereas flywheels can handle a pretty severe duty cycle."
A report for the U.S. Department of Energy also states that [12]:
“Flywheels and supercapacitors, with their high cycle life and ramping capabilities, are good candidates for regulation. Batteries may be better for supplying load following, where cycle life requirements and the ratio of peak power to stored energy are lower.”
3
FLYWHEEL ENERGY STORAGE
3.1 General
A literature review was conducted to find out the state of the art in flywheel systems. System design, storage capacity and materials used were investigated.
To secure the reliability of the literature review information was gathered from multiple sources. These include articles retrieved from international recognized databases, such as IEEExplore, Science Direct and cited books relevant to the subject.
3.2 History
The use of flywheel to store energy is not a new technology. Basic flywheels such as stone wheels were used to craft pottery thousands years ago. The stone wheel smoothens the pulsed power from the foot and enabled a smooth rotation of the pottery turntable.
Under the industrial revolution the use of the flywheel increased significantly when the steam engine was introduced. During this period technological development of flywheels started. The first milestone was when Dr. A Stodola showed that certain shapes yield uniform stress distribution for isotropic materials. The next milestone in flywheel development took place during 1970’s when applications for backup-power and electric vehicles were proposed. During this period flywheels made of composite material was proposed and built. The development continued during the 1980’s when magnetic bearings were introduced. Recent developments in materials, magnetic bearings, microcomputers and power electronics have made it possible to consider flywheels as competitive option for electric energy storage [14, 21].
3.3 Flywheel basics
Flywheels store energy in kinetic form. The energy is stored in a rotating mass and the amount of energy stored is a function of the moment of inertia and angular velocity, as shown in equation (3.1).
(3.1)
is the moment of inertia and is the angular velocity. The moment of inertia is determined by the shape, principal rotational axis and mass of the flywheel and is defined by the following equation.
(3.2) Where is the distance from the rotational axis of the differential mass .
12 Equation (3.1) state that greater gain in stored energy come from increasing the angular velocity, rather than increasing the moment of inertia. This is because the stored energy scales with the square of angular velocity and only linearly with the moment of inertia. As an example a flywheel with the shape of a thin rim ( where is the outer radius and is the inner radius) is considered. All the mass is concentrated at the infinitely thin outer rim. Thus from equation (3.2) the moment of inertia is given by
(3.3)
where is the mass and is the radius of the flywheel. The stored energy is given by
(3.4)
The amount of stored energy is limited by the tensile strength of the material. If the stresses in the flywheel exceed the tensile strength of the material the flywheel will break apart. The limiting stress in a thin rim is the tangential stress, which is given by equation (3.5) [15], where
(3.5)
is the maximum tensile strength and is the material density. From equation (3.4) and (3.5) the
maximum energy density and specific energy for a certain material can be obtained. Thus the specific energy and energy density for the thin rim flywheel can be expressed as
(3.6)
(3.7)
From equation (3.7) it is clear that a material with high tensile strength is a requirement to obtain high energy density. However for most applications the total mass of the system must be taken into consideration which is considered with the specific energy of the flywheel, as described by equation (3.6). This analysis of a thin rim flywheel shows that the specific energy is proportional to the maximum tensile stress of the material divided by the mass density of the flywheel material. Equation (3.6) shows that a high strength material with low density would be optimal for flywheels rotors. The factor in equation (3.6) and (3.7) is only valid for a flywheel with the shape of a thin rim.
A flywheel made of high-density materials, such as steel, would indeed store more energy than an equivalent size flywheel of low-density material at equal angular velocity. However low density materials develop lower internal stresses, which allow higher angular velocities. This enables designs that store same amount of energy at a lower weight, enabling compact system design.
3.3.1 Geometries and material
A more general expression for the maximum specific energy and energy density given by
(3.8)
(3.9)
Where is the so-called shape factor and can be described as a measure of how efficient the material of the flywheel is used. For a detailed derivation of the shape factor see [17]. Figure 3.1 shows the most common types of flywheel geometries.
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Figure 3.1 Shape factor of common flywheel shapes [16]
The Laval disk (named after the Swedish engineer Gustav de Laval) has a shape factor of K = 1. This disk has the properties such that the radial and tangential stress components remain equal throughout the entire disk. Depending on the material used the optimal flywheel shape will differ. Isotropic materials, such as steel, have equal strength in both the tangential and radial direction [16]. Anisotropic materials, like fibre-reinforced composites, have unidirectional tensile strength, i.e. are stronger in the longitudinal fibre direction. As shown in Figure 3.1 there are shapes better suited for these types of materials. A thin rim (hollow circular cylinder) flywheel is a very good candidate for composite material as this geometry exploit the high unidirectional strength of the fibres [16, 17]. Multiple sources [18, 16,15] state that a hollow circular cylinder is the optimal shape for a composite flywheel rotor.
Table 3.1 Rotor material comparison [15,16]
Material Density [kg/m^3] Tensile strength [GPa] Specific energy [Wh/kg] Steel 4320 Steel 7700 1.52 50 AISI 4340 7800 1.80 64 Alloy AlMnMg 2700 0.60 62 Titanium TiAl6Zr 4500 1.20 74 Composites E-glass 200 0.10 14 S-Glass 1920 1.4 210 Carbon T-1000 1520 1.95 350 Projected composites 1780 10 780
Table 3.1 show the properties of different rotor material. Maximum specific energy is calculated with equation (2.9) with . The data in the table shows, as already described above, that the best material for a flywheel rotor is a high strength material with low density. Composite materials have both high strength and low density and are ideal for flywheel rotors used for energy storage. A composite material allows a higher rotational speed and this result in flywheel rotors with high specific energy. Composite materials are therefore a better choice than metals when designing flywheel rotors. The theoretical specific energy of composite rotors is around five times higher than metallic ones [20]. The high-speed flywheel concept originated in the early 1970s. A researcher at Lawrence Livermore National Laboratory presented an article in Scientific American proposing a new approach to rotor design, recommending the use of composite materials instead of metal [21].
14 Composite materials also have safety advantage over metallic material. If a potential failure at high angular velocity and the radial stresses exceed the material strength composite flywheel is less likely to break apart in free flying projectiles. Instead circumferential cracks develop and the flywheel breaks apart gradually.[4]
3.4 Flywheel systems components
Basically, a modern flywheel energy storage system (FESS), consists of five key components; 1) flywheel rotor, 2) bearings, 3) electrical machine, 4) power electronic interface, and 5) housing.
3.4.1 Electrical machine
The energy is stored in the flywheel, as presented in section 3.3, and in order to charge and discharge the flywheel must be coupled to an electrical machine. When the flywheel is charging the machine accelerates the flywheel and when energy is extracted the machine slows the flywheel down. Thus the electrical machine must be able to operate as both a motor and a generator. In [18] a design is described with separate motor and generator, however the typical design of a FESS is to use only one machine.
The key design criteria that the machine must meet include high efficiency, high power density, low idle losses and low rotor losses. High efficiency is an important requirement for FESS to be an effective energy storage system. Low rotor losses are critical since most FESS operates in vacuum and the heat removal is limited. Low idle or stand-by losses are desirable for energy storage over longer times.
Common types of electrical machines used in FESS include: the induction machine (IM), the switched reluctance machine (SR) and the permanent magnet synchronous machine (PMSM) [22]. A summary of the main properties of these machines is summarized in Table 3.2
Table 3.2 Advantages and disadvantages of common electrical machines in FESS [15, 16,22].
Advantages Disadvantages
PMSM + No need for excitation - Risk of demagnetization
+ Rotor design complexity reduced, no need for electric wiring
- Electromagnetic spinning losses at zero torque
+ High overall efficiency possible - Low-strength of PM material require structural support against centrifugal forces + Highest power density - Sensitive to heating
IM + Demagnetization impossible - Poor overload capability + Possibility to control excitation field, no
electromagnetic spinning losses
- High maintenance + Can be built with low-cost high-strength
materials
- Adds complexity to the rotor design, due to the need of wiring
- High losses due to the need of excitation
SR + Very robust - Low power factor and low power density - Need of excitation
+ No idle losses - High rotor eddy current losses
In most high-speed flywheel energy storage systems PMSM is chosen due to superior properties when it comes to power density and efficiency.
3.4.2 Bearings
The rotor must be supported by bearings. The bearings minimize the friction and keep the rotor in place. In most modern flywheel designs high speed is desirable, implying extensive requirements on the bearings. The bearings must have low losses in order to run the flywheel system efficient.
15 Mechanical bearings are the best choice for FESS with speed under 20000 rpm and with speeds over 40000 rpm magnetic bearings are the only option [19]. Mechanical bearings offer straightforward implementation and low initial cost but relative high friction. The need of lubrication makes these types of bearings unsuitable for high-speed flywheel systems. As later will be discussed, high speed flywheel are operated in low-pressure environment, therefore lubrication of mechanical bearings is hard to implement [23].
Magnetic bearings are not in contact with the rotor or shaft and offer low losses, long lifetime and require no lubrication. These properties make magnetic bearing suited for use in high-speed flywheel systems. Basically, a magnetic bearing consists of permanent magnets that levitate the mass of the flywheel and controlled electromagnets that stabilize the flywheel rotor radially. The stabilization requires a complex control system, with expensive sensors. A combination of both mechanical and magnetic bearings is used in some systems [15].
High temperature super-conducting magnetic bearing (HTS) is a recently developed type of bearing which significantly lowers the losses [16]. With this type of bearing a control system is not needed but the bearing system requires cryogenic cooling [15]. These types of bearings are still under research and development by Boeing in 2011.
Table 3.3 Comparison of different types of bearings [27].
Bearing type Approximate
power loss
Advantages Disadvantages
Ball
(mechanical) 5–200 W + Simple, low cost, compact - Needs lubrication, seals, hubs and axle.
Magnetic 10–100 W + Acts directly on rotor,
allows high speeds.
- High cost, requires ‘‘touchdown bearings’’ and reliability uncertainty.
HTS 10–50 W + Low loss, high forces - Long-term development requirement, housekeeping losses (cryogenic cooling)
3.4.3 Housing
One of the more important parameters of FESS is efficiency. The aerodynamical drag loss contributes largely to the total system losses [24], as these losses increase with the cube of the rotational speed. Therefore, the losses will be significant if a high-speed flywheel is operated in atmosphere pressure. Therefore reduction of these losses is an effective way to reduce total losses of the overall system efficiency. One solution to reduce the aerodynamically drag loss is to mount the flywheel in a vacuum housing. This eliminates air drag and thereby reduces the losses. However, this adds complexity to the overall system and requires auxiliary system such as vacuum pump and a cooling system. A vacuum environment may require a more efficient cooling system that can handle heat removal from the electrical machine and other part of the flywheel system that produces heat, since the heat transfer is less effective in vacuum.
Another approach is proposed in [24]. Instead of operating the flywheel in low pressure it is shown that by using a gas-mixture of helium and air can be another effective way to reduce aerodynamically drag loss. One advantage is that the requirement on the cooling system is reduced.
The task for the housing is not only to reduce losses; it must also withstand a potential failure. If the rotor breaks apart the housing chamber must be able to stop free flying projectiles. The housing is typically thick steel or other high strength material. The safety can be enhanced by multiple-barriers. The flywheel system
16 can be installed underground where a thick steel housing can provide a first protection and a second barrier is provide by the underground installation [26].
3.4.4 Power electronic interface
In modern FESS, power electronics are a vital part of the system. It provides a control interface for the electrical machine and interface for the power transfer. The power electronic interface usually consists of a bi-directional inverter/converter and a variable speed drive. The power from/to the flywheel is available at a DC-link. To interface the FESS to an ac-grid, another bi-directional converter is needed, i.e. the converter may be single-stage (AC-DC) or double-stage (AC-DC-AC).
The generator will produce AC current with decreasing frequencies as the flywheel slows down. It is therefore needed to convert the AC current to a constant frequency; this is done by the power electronic interface. Depending on requirements of the FESS application the controller operation of the converters may vary. For a FESS interconnected with an ac-grid, control of both active and reactive power may be needed.
Desired attributes for the power electronic interface are high power capability, high switching frequency and high efficiency. With the recent development of semiconductors, rectifiers and power converters can meet high power ratings and efficient demands. The converter is usually based on insulated-gate bipolar transistors (IGBTs). The power electronic components are compact which make it possible to house them in a unit that is comparable to the flywheel unit itself [15].
3.5 Range of Capacities
When it comes to the power and energy capacity of a FESS it is important to point out that these are completely decoupled. This fact can be shown by equation (3.9), the specific energy of the flywheel is set by four mechanical parameters: Shape, strength of material, mass density, and angular velocity. The electrical machine and the power electronics is not part of this equation and therefore do not affect the energy stored in the flywheel. However, the rotor of the electrical machine does indeed add to the total amount of stored energy but generally it contributes significantly less than the actual flywheel. Furthermore, the power level of the system depends mainly on the properties of the electrical machine and the power electronic interface. Thus the systems energy storage capacity is limited by the mechanical properties (mainly rotational speed limit of the flywheel) and the limit for the power capacity is set by the electrical machine and power electronics.
Individual flywheels with the storage capacity up to 138 kWh have been stated in literature [15]. However, to the author’s knowledge, the range of stored energy for commercially available FESS is 0.2 – 25 kWh. It should be pointed out that several flywheel units can be connected in parallel/series to increase the storage and/or power capabilities.
The data for the specific energy in presented in Table 3.1 is only considering theoretical limit of the flywheel rotor. Specific energy for a complete system must take the all the system components into consideration, which will imply a decreased specific energy for the entire system. Commercially available FESS today has specific energy significantly lower than the values presented in Table 3.1[26]. With the development of new high strength materials, which enables higher speeds the specific energy for the complete system will increase. According to [27] FESS with specific energy up to 200 Wh/kg and specific power up to 30 kW/kg is expected in the next few decades.
3.6 Environmental issues
The materials used in FESS are generally non-hazardous. The materials used are mainly; composite-fibres (carbon-, glass- and epoxy-fibers), steel, copper, aluminium, silicon and rare earth magnates. Under normal operation there are close to-zero emissions. If properly handled all materials used can be re-cycled at end-of-life [4]. The main hazardous concern is the potential failure of the flywheel rotor.
3.7 Commercially available flywheel systems
There are a number of companies around the world that manufacture flywheel energy storage systems. This section provides an overview over some of the systems that are commercially available today.
17 Flywheel energy storage systems are usually categorized as either low-speed or high-speed. The border between these two types is found around 10 000 rpm [7]. Low-speed flywheels have long been commercially available, these systems typically utilize metal rotor and are characterized by low energy density. The most common application for low speed flywheels is to act as a power quality device to provide ride-through of interruptions up to 15 s long or to bridge the shift from one power source to another. Examples of leading commercial manufactures of low speed flywheels are Piller and Active Power [24].
The current R&D on flywheel energy storage systems has focused towards high-speed composite machines, running at rotational speed over 10,000 rpm. As shown above the high directional strength properties of composites materials, combined with their comparatively low density, allows optimal design of the overall system with respect to specific energy [29]. Examples of leading commercial manufactures of high speed flywheel systems are Beacon Power and Vycon Energy [28,29].
3.7.1 Beacon Power
Beacon Power Corporation, based in Massachusetts, USA, aims to develop advanced flywheel-based energy storage systems. Their first systems was backup power solutions for telecommunication application but the focus have now changed towards development of grid-scale flywheel energy storage system for applications such as grid-scale frequency regulation service.
Beacon Power's main product is the “Smart Energy Matrix”, based on a concept of a multi-flywheel energy storage system. This system consists of multiple 100kW/25kWh flywheel units. The main components of each flywheel unit are the following [29]:
- Rotor assembly – Composite flywheel, metal hub and shaft, interface for active lift and magnetic bearing system, motor rotor
- Motor/generator – Permanent magnet machine - Magnetic bearings and active lift system - Vacuum system
- Vacuum housing – Structural support for the rotor assembly and low-pressure vessel.
Figure 3.2. Conceptual overview of Beacon Power Flywheel System [44].
Each flywheel unit is coupled to a bi-directional power converter, which acts as an inverter and variable speed motor drive. The power converter provides a DC interface which makes it possible to connect multiple units in parallel to a common DC bus bar in order to meet higher power demands, as shown in Figure 3.3.
18
Figure 3.3 Multiple flywheel units parallel connected to a common DC bus bar.
Beacon Power has a 20 MW test “Smart energy matrix”-plant in operation, located in Stephentown, USA. The purpose of this plant is to provide frequency regulations services. This plant is comprised of 200 parallel-connected 100kW/25kWh flywheel units. The speed range of the rotor is 8000 – 16000 rpm. The plant can provide a maximum output power of 20 MW for 15 minutes. The response time is <4 seconds, input/output voltage is 480 V three phase AC, 50 / 60 Hz [25].
Figure 3.4 Left: Beacon Power 20 MW Smart energy matrix test facility. Right: Close up of flywheel unit. [26]
3.7.2 Vycon Energy
Vycon market a system with product name VDC-XE which consists of a high speed steel flywheel with a speed range of 14,500 -36750 rpm. The flywheel is coupled to a high-speed motor/generator that interfaces via power electronics to a 400-600 V DC-link. The maximum output power for one unit is 300 kW. Discharge time at rated output is around 14 s. It is possible to parallel several units to increase power output and/or discharge time.
Vycon targets the UPS market segment and the flywheel system can be an alternative to lead acid batteries. Another application is in the railway industry (traction applications). The flywheel system absorbs breaking energy from the train, which can be used when the train accelerates. This can give subway operator a way to lower their energy consumption. Vycon also market their flywheel system for usage in large cranes. The use is similar to traction system, breaking energy is stored in the flywheel and released when the crane needs power to lift [29].
3.7.3 Piller
Piller is another company that provides flywheel based UPS solution and load levelling in local grids, such as traction applications. Piller flywheel technology is based on a low speed steel flywheel with a speed range of 3,600 to 1,500 rpm. The electrical machine is a high power synchronous machine with a maximum power rating of 1.65 MW. The maximum discharge time is around 10 seconds [31].
19
3.7.4 Active Power
Active Power provides flywheel based UPS solutions. The core technology is a vacuum operated low speed flywheel with a power rating of 250 kW. The flywheel is made from forged steel and has an operational rotational speed range of 2500-7700 rpm. The system utilizes a combination of ceramic ball bearings and magnetic lift to increase bearing lifetime. The power is available either at a DC-link or AC-terminal. One single flywheel unit can provide the nominal output power if 250 kW for 14 seconds. The standby efficiency is 99,8%. Modular system design, were multiple flywheel units is parallel connected can provide power up to 2 MW [32].
Figure 3.5 Active Power flywheel unit.
3.7.5 Market summary
As seen on the examples above the flywheel market is focusing on UPS and traction system. With exception for Beacon Power all companies mentioned above are competitors in the UPS solution market. These systems are mainly for power quality application where long discharge times not are needed. At present and to the author’s knowledge, Beacon Power the only company focusing on grid-scale solution.
Table 3.4 Manufactures of flywheel systems [29,30,31,32].
Manufacturer Rated power [kW] Discharge time [s] Rot. Speed [rpm]
Low Speed Active Power 250 14 2500-7700 Piller 1650 10 1800-3600 High Speed Vycon Energy 215 14 14500-36700 Beacon Power 100 900 8000-16000
20
3.8 Summary
Features that flywheel energy storage systems include: - High power density
- Relative high specific energy density
- Low or no capacity degradation during discharge/charge. – Flywheel have very high cycling capacity, up to 90 000 charge-discharge cycles have been reported.
- Easy to measure the state of charge - Function of the rotational velocity.
- Very low maintenance – Manufactures claim that flywheel have close to zero maintenance. - Quick response time
- Scalable and no geological barrier - Low environmental impact
21
4
MODEL DESIGN
4.1 SCOPE
In this thesis the first steps in the development of simulation FESS model were taken. The essential components have been identified which are needed for simulating a FESS system. The model is built using the electromagnetic time domain transient simulation environment PSCAD/EMTDC. The model can later be used for evaluating a grid connected FESS capability to handle various power quality problems or other applications in electrical grids. The model is later verified with usage in a peak shaving application. The model developed is further described in appendix A1.
The model and control system is built using standard components from the PSCAD/EMTDC master library. The focus will be on the power electronic interface. In a real system multiple parallel-connected power converters are needed to meet the power requirements, however to simplify the developed model one power converter module is considered.
4.2 Model description
The developed model of a the flywheel energy storage system (FESS) include the following components - Two voltage source converters (VSC)
- Permanent magnet synchronous machine (PMSM) - Step-up transformer
- Grid
The VSC connected to the PMSM (machine-side VSC) provides a variable speed control for the PMSM while the grid connected VSC (grid-side VSC) control the DC-voltage of the DC-link. The VSCs are formed by six Insulated Gate Bipolar Transistors (IGBTs). The VSCs are back-to-back connected to enable bidirectional power flow. The grid is modelled as a voltage source.
M/G
FW
~
=
~
=
~
Step-up transformer Grid VSCs
PMSM Flywheel
Figure 4.1 Model topology
4.3 Sinusoidal pulse width modulation
In order to produce the desired AC output from both VSC, sinusoidal pulse width modulation (SPWM) is performed. The output from the VSC is a square wave with two possible voltage values: +Vdc/2 or –Vdc/2. The three phase converter bridge consists of six switches, each formed by an IGBT with an anti-parallel diode. The anti-anti-parallel diodes provide protection for peak load inductive current when the switch is off.
22 A schematic view of the VSC is shown in Figure 4.2. The gate signals for controlling the switches (G1-G6 in figure 4.2) are generated by comparing a triangular wave (carrier) with a sinusoidal wave (desired phase voltage reference), as shown in Figure 4.3.
Figure 4.3 Voltage reference for phase A, B or C and triangular wave
When the instantaneous value of reference voltage is greater than the triangular wave the gate signal is 1 and 0 when the voltage reference is less than the triangular wave. This signal controls switch G1 and the inverse signal controls switch G4. The configuration of the switches is shown in Figure 4.2.
The gate signals are generated in the same manner for all three phase, the voltage reference for each phase is compared with the triangular wave and the gate signals for the corresponding switch is generated. G1 and G4 corresponds to phase A, G3 and G6 to phase B, G5 and 62 to phase C.
The output voltage for the VSC is not a perfect sine wave and will contain voltage components with higher frequencies than the desired fundamental frequency. However the undesired harmonics can be reduced by using an appropriate filter, for example a low-pass filter. The amplitude of the output voltage is governed by .
is the modulation index, with is always less or equal to 1.
4.4 D-Q-0 Transformation
The mathematical analysis of three phase system can be complicated; however there exists methods to simplify the analysis of such systems. One of these methods is the dq0 transformation. This transformation simplifies the analysis and derivation of control systems of three phase synchronous machines and power converter and will be used in the following sections.
The dq0 transformation is a mathematical transformation used to transfer stationary three phase (abc) quantizes to three rotating quantities (dq0). In balanced three phase systems the 0-componets can be neglected, and the dq0 transformation can be reduced to d- and q- components. In this thesis only balanced system are considered. The d- and q-components are time invariant (DC quantities). The abc-dqo and the inverse dq0-abc transformation are performed according to the following matrix equations.
(4.1a) (4.1b)
23 Where , are the dqo components, , , are the three phase components and is the reference angle to the stationary three phase component . The d,q components are rotating with the rate of change of the angular position. In Figure 4.4 a graphical representation of the dq transform is shown.
θ xa xb xc xq xd dθ/dt
Figure 4.4 Graphical representation of the dq-transformation.
4.5 Motor/generator
The motor/generator is modelled with a permanent magnet synchronous machine (PMSM) model from the standard PSCAD library. The model is a linear state model in the d-q rotating reference frame; the equations of the PMSM are expressed in the d-q reference frame to transform the nonlinear equations three phase equations to a linear state model [33]. The dq representation also simplifies the implementation of the control system. The stator voltages is given by the following equations
(4.2)
Where and are the d- and q-axis stator inductances, respectively. is the angular velocity of the
rotor, are the stator currents and is the rotor flux. The electromagnetic torque can be calculated
with the following equation [33]
(4.3)
Where is the torque and is the number of magnetic poles in the rotor. The machine considered has two magnetic poles, which implies that the electrical frequency is equal to the angular frequency of the machine rotor. The maximum torque is achieved by keeping, , hence the electromagnetic torque is given by [33]
24
4.5.1 Machine-side VSC control strategy
The PMSM control is based on vector control, also called field oriented control. This control method consists of controlling the stator currents. The goal of the vector control is to separately control the torque producing and magnetizing flux components of the stator current. To achieve this decupled control, the d-axis component of the stator current is aligned with the rotor flux. This leads to a control structure similar to the control of a DC-machine. In Figure 4.5 the block diagram for the PMSM control implementation is presented.
The control system consists of the following subsystems: - Current measurement
- Rotor angle and speed measurement - Current control PMSM ABC to dq Current Control ABC to dq PWM Isdref* vsq ref* vsd ref* isq G a te S ig n a ls i s a i s b i s c isd Rotor angle and speed messurement θr ωr vsa r e f * vsb r e f * vsc r e f * θr Isq ref*
Figure 4.5 Vector control of the PMSM.
The stator currents are measured ( , ,, ,) and transformed from abc to the rotating d-q reference frame
( , ). To keep the d-axis aligned to the rotor flux, the rotor angle (θ) is used in this transformation. To
control the stator currents a current control is derived from equation (4.2) Laplace transform yields
(4.5)
The current controller can be formed by a feedback loop as shown in Figure 4.5. The error between the reference stator currents and and the measured stator currents are processed by a PI
controller. As shown in equation (4.5) is the d- and q-axis stator currents components are coupled and needs to be cancelled to achieve a functioning current control. In order to keep the d- and q-axis components of the stator reference voltages synchronized to the rotor, the rotor angle (θ) is used in the d-q to abc transformation. The coupled machine dynamics are added to the output signal from the controller which results in the voltage reference signals ( ). The voltage reference signals passed the
25 ωrΨm + -+ -ωrLsqisq isd ref* isd PI vsd ref* + - + + ωrLsdisd Isq ref* isq PI vsq ref* +
Figure 4.6 Current controller.
The reference currents passed to the current control is calculated either by a speed controller or power controller. The speed controller is implemented as shown in the following block diagram
ω*
ω
PI
-+ Isq ref*
Figure 4.7 Speed controller.
As shown in Figure 4.7 the speed controller calculates the q-axis current reference signal ( ), which is proportional to the torque according to equation (4.4), by finding the difference between the reference speed (ω*) and the measured speed (ω). The PI controller process the error in order to achieve accurate control.
The power controller also calculates a q-axis current reference signal. Since the power developed when the flywheel deceleration is given by
(4.6)
Where is the angular velocity of the flywheel, is the power reference and is the torque. The torque required to keep a constant power output can be calculated as
(4.7)
Assuming a stiff shaft coupling between the flywheel and generator, the mechanical power is equal the electrical power, . The q-axis current reference, , can by calculated by combing equation (4.7) and (4.4).
26 P* P
PI
1/ω 3/2 1/Ψ-+
isq ref*Figure 4.8 Power controller
The power controller is implemented as shown Figure 4.8. The error between the reference power (P*) and the measured power (P) is processed by a PI-controller in order to achieve accurate control.
4.5.2 Grid connected VSC Model
The objective of the gird-side converter is to keep the DC-link voltage constant regardless of the magnitude and direction of the PMSM power output. The control system shown in Figure 4.9 consists of the following subsystems: - RMS voltage measurement - Current measurement - DC voltage control - Current control - Phase-locked loop (PLL) id iq Current Control
~
Transfomer Grid ABC to d-q iq ref*= 0 id ref* PWM G a te S ig n a ls d-q to ABC vtq ref* vtd ref* Rf Lf vsd vsa vsb vsc vta vtc vtc Vdc Control vdc Vdcref* vdc PLL va r e f * vb r e f * vc r e f * θp ita itc itbFigure 4.9 Complete control system of grid-side VSC
The AC-dynamics of the VSC model in the stationary three phase (abc) can be described with the following equations. (4.9)
27 Where are the output voltages from the VSC, , are the grid side voltages , , ,
are the three phase currents. is the interface resistance and is the interface inductance.
4.5.3 Grid-side VSC control strategy
Transforming equation (4.9) to the rotating dq reference frame synchronized with the grid voltage yields [36]. (4.10)
Where and are the output voltages from the VSC, and are the grid side voltages, and are the output d-axis q-axis currents components and is the system frequency in radians per second. With the dq-reference frame synchronized to the grid voltage ( ) d- and q-components become:
(4.11)
The d- and q-axis currents in equation (4.9) are coupled with the terms and respectively. In
order to derive independent current control loop for the d-axis and q-axis currents these terms must be cancelled. Equation (4.8) transformed to the laplace-domain gives
(4.12) By denoting (4.13)
and based on the decupled compensator model presented in [34] the VSC model can be described by two decupled first order systems as shown in Figure 4.10.
1 ---sLf+Rf Itq utq 1 ---sLf+Rf Itd utd
Figure 4.10 Decoupled VSC model.
The VSC can now be controlled with the input signals and . These input signals, and are computed by subtracting the reference currents value ( and ) by the measured current (
and ). The error is processed by a PI controller and outputs and .
From these signals the VSC terminal voltage references ( are computed be adding the compensation terms according to equation (4.13). The terminal voltage references are then passed to the PWM, which outputs the gating signals to the IGBT bridge. In order to synchronize the frequency of the terminal voltage with the grid frequency, the phase angle of the grid voltage is obtained from the phase-locked loop is used in the dq-abc transformation of the voltage references passed to the PWM.
28 The derived control loops are capable of separately controlling the d- and q-axis currents, as shown in Figure 4.11. + - + - + ωLfitq vsd Itd ref* itd + -ωLfitd itq + -PI PI Itq ref* utd utq vtd ref* vtq ref*
Figure 4.11 Grid-side VSC current controller.
The DC-link voltage is controlled by exchanging active power between the grid and the VSC by controlling
the DC-link voltage can be controlled [38], hence the DC-voltage controller generates a d-axis current
reference signal . The error between the reference DC-voltage value and the measured DC-voltage is processed by a PI controller, as shown in Figure 4.12. The output is limited to make sure the current reference is kept in safe operation range of the VSC.
+ -Vdc ref* Vdc Itdref* PI
Figure 4.12 DC voltage control
The reactive power can be calculated with the following equation, with as stated in equation (4.11)
(4.14)
Hence the reactive power is controlled by the q-axis current. The q-axis current reference signal is set equal to zero in order to maintain unity power factor [35].
4.6 Flywheel
The flywheel is modelled as inertia added to the PMSM rotor. The flywheel is assumed to have a direct connection between the motor/generators rotor shaft. The dynamics of the rotor/flywheel is modelled with the following equation
(4.15) Where is the electromagnetic torque, is the mechanical losses, is the angular velocity of the flywheel, is the damping coefficient and is the inertia of the flywheel.
